I assume that means they are offering that if someone hacks a bitcoin wallet and gives them the proceeds, they will share a fraction of the stolen assets.

I'd assume that what they're saying is: if you provide information that lets them identify Hufflepuff, and they successfully sue him for the money, then they'll reward you.

My interpretation doesn't require you to have control of the bitcoins at any point, and also explains why they provided their information about the guy.